Warring Contextualities - Provably Classical vs Provably Nonclassical

Abstract:In the literature, there are two differing definitions of contextuality: Kochen and Specker's, and Spekkens' (or ``generalised''). However, researchers using one of these definitions rarely consider the other, meaning comparative analysis of these two notions is rare. In this paper, we advance the idea that Kochen-Specker contextuality provides a generalisation of the idea of system being fundamentally \emph{nonclassical}, while Spekkens' noncontextuality provides a generalisation of the idea of a system being \emph{classical}. This allows us to reconcile the two approaches, as different stages in a hierarchy of classicality/nonclassicality.

16+13 pages, 2+1 figures. v2. Fig 1a fixed, added brief discussion of related results for (un)steerability

Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)

arXiv:2604.14319 [quant-ph]

(or arXiv:2604.14319v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.14319 Focus to learn more arXiv-issued DOI via DataCite

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